Caden had ¹₂ as many beads as Gabriel. Gabriel had ²₃ as many beads as Winnie. After Caden and Winnie gave 28 beads to Gabriel, Gabriel had four times as many beads as Caden. Winnie then had the same number of beads as Gabriel.

1. What was the ratio of the number of beads Winnie had to the number of beads Caden had in the beginning? Answer in simplest form.
2. How many beads did Gabriel have in the end?

Caden	Gabriel	Winnie
1	2
	2	3
1	2	3

(a)
The number of beads that Gabriel is repeated.  

Ratio of the number of beads that Winnie had to the number of beads that Caden had in the beginning = 3 : 1

	Caden	Gabriel	Winnie	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 28	+ 56	- 28
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of beads at first and in the end remains unchanged. Make the total number of beads the same. LCM of 6 and 9 is 18.

Number of beads that Gabriel received from Caden and Winnie
= 2 x 28
= 56

Number of beads that Gabriel received from Caden and Winnie
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of beads that Ashley had in the end
= 8 u
= 8 x 14
= 112